The linguist Noam Chomsky once suggested that our ignorance could be divided into two categories: problems and mysteries. Problems are difficult questions on which we have some sort of grip: work remains to be done, key insights are still lacking, the gleams of final understanding have not yet penetrated our intellectual gloom, but we are beginning to ask the right questions, and we may have some useful data to build on.
Mysteries, on the other hand, are so obscure that we do not know where to start looking—we may not even know what an answer might look like. For example, the age of the universe may be considered a problem, on which we fancy we have made considerable progress, though questions remain. The origin of the universe is a mystery.
Moving from theories of epistemology to our topic of chess improvement, I was struck recently by how idiosyncratic my own chess understanding is. To be blunt, my understanding of chess is like Swiss cheese, with more holes than cheese. Yet at times, the quality of the cheese is surprisingly good, belying my current 1900 USCF rating.
The position above and the label “very difficult” are from p. 29 of IM Willy Hendriks’s stimulating book Move First, Think Later (New In Chess, 2012). Every chapter in the book starts with several diagrams which the reader should try to solve, writing down his proposed solutions. It is important the reader do this, not only for the chess benefit to be derived from studying the problems, which are worthy in themselves, but also because the author uses the problems as logical points of departure for the narrative in each chapter. The author considers the above diagram unusually difficult to solve. He devotes eight pages to discussing the relevant ideas, crowning the discussion with the gamelet in which the motif appeared. The chapter is titled “My most beautiful move.” He writes: “Two things are slightly regrettable about the most beautiful move of my career: a) I didn’t think of it myself (Fritz did) and b) I didn’t manage to play it (though I came close). But it is a very surprising and very beautiful move, so I like to present it as my best move ever, although my merit mainly consisted in looking at Fritz’s display at the right moment (and understanding that something beautiful had turned up).”
When I looked at the diagram, I did not have any special trouble understanding the key ideas or what needed to be done. It took me about a minute to find the solution. Maybe a little less, but let us say a minute. Of course, I had the important advantage of knowing the diagram had a solution before I started thinking, but even so, it is clear that the label “very difficult” was not at all accurate in my case. And yet objectively speaking, I am not a very good player. (Spoiler alert: I will give the solution at the end of this post.)
By way of contrast, consider this position from p. 13 of Move First, Think Later:
Remember Chomsky’s division of ignorance into problems and mysteries? The first diagram was a problem for me, and not much of one at that. But this latter diagram was a mystery. Think about it yourself for a minute or two.
The longer I looked at the position, the less I understood it. White has a queen and bishop battery pointed at the kingside, and the Rf1 has an open file leading down the board to f7. Some sort of kingside attack seemed indicated, but I could find no concrete way to proceed. Part of the reason for my bafflement, I think, is that this was the first chapter; I did not yet realize that most problems in this book were more sophisticated than those in my well-worn books by Fred Reinfeld and Al Horowitz, whose diagrams usually had a satisfying, red-blooded, all-American tactical solution (except for a few I had cooked).
So I gave up on this diagram, turned the page, and started reading. The position turned out to be from Kasparov-Shirov, Wijk aan Zee 2001. Kasparov played 17 a4! here, preparing Ba3 to chase away the black rook from f8. Perhaps if this position had occurred in one of my own games, 17 a4! would have occurred to me in context, but looking at the position cold, I did not even dream of such a move as a “solution” to the position. A pawn move preparing a piece move to threaten an enemy piece that could move away—preposterous! And yet I imagine this kind of “solution” is far more common in practical play than clear-cut combinations to win decisive amounts of material.
Returning to the first diagram above: did you find White’s idea? Black seems to be winning, because the white queen is under attack and must retreat, but all retreats seem to lose the white knight on e5. I thought, “I would like to play Ng6+ opening the h-file, because then I could mate if I could check on the h-file.” But after 1 Ng6+ hxg6 there are no checks on the h-file. White has lost the knight, and after he moves his queen (which is still under attack), the bishop on f7 will also fall. So I have to move the queen at once. Where do I put it? Then I saw the winning idea: 1 Qg3!! If 1…Nxg3, 2 Ng6+! now works: 2…hxg6 3 hxg3+. The desired check on the h-file appears, and White mates. The loss of White’s queen is of no consequence. Of course Black does not have to fall into this mate, but whatever he does, White will keep an edge, according to the author. (I do not pretend to have analyzed Black’s other possible lines.)